School of Mathematics and Statistics
Southwest University
Chongqing 400715, China
email: shbdeng@swu.edu.cn
School of Mathematics and Statistics
Southwest University
Chongqing 400715, China
email: fanylimath@163.com
Shengbing Deng, Fanyun Li
Abstract:
In this article, we study a fractional Laplace equation on a compact
Riemannian manifold involving a Hardy potential and a nonlinearity with
critical exponent,
$$
(-\Delta_g)^s u - \mu \frac{u}{d_g(x, x_0)^{2s}}
= \lambda f(x)|u|^{p-2}u + k(x) |u|^{2_s^*-2}u \quad \text{in } M,
$$
where \( n > 2s \), \( s \in (0,1) \), \( 2 < p < 2_s^* \), and
\( 2_s^* = \frac{2n}{n-2s} \) denotes the fractional Sobolev critical exponent.
Under suitable conditions on the parameters \(\mu, \lambda\) and the smooth positive
functions \( f \) and \( k \), we employ critical point theory to establish the
existence of nontrivial solutions.
Submitted February 9, 2026. Published May 14, 2026.
Math Subject Classifications: 35R09, 35R11, 35A15, 35J60.
Key Words: Fractional Laplacian; Hardy potential; critical exponent; compact Riemannian manifold.
DOI: 10.58997/ejde.2026.38
Show me the PDF file (453 KB), TEX file for this article.
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Shengbing Deng School of Mathematics and Statistics Southwest University Chongqing 400715, China email: shbdeng@swu.edu.cn |
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Fanyun Li School of Mathematics and Statistics Southwest University Chongqing 400715, China email: fanylimath@163.com |
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